On Singular Interval Systems

We consider the interval iteration [x]kH = [A][X]k+ [b]with p(I[A]I) ::; 1 where I[A]I denotes the absolute value of the given interval matrix [A]. If I[A]I is irreducible we derive a necessary and sufficient criterion für the existence of the limit [x]*= [x]*([x]o)of each sequence ([xt) of interval iterates. In this way we generalize a well-known theorem of O. Mayer [6] on the above-mentioned iteration, and we are able to enclose solutions of certain singular systems (I A)x = b with A E [A] and degenerate interval vectors [b]==b. Moreover, we give a connection between the convergence of ([X]k) and the convergence of the powers of [A].